Linear Mixture Models, Full and Partial Unmixing in Multi- and Hyperspectral Image Data

As a supplement or an alternative to classification of hyperspectral image data the linear mixture model is considered in order to obtain estimates of abundance of each class or endmember in pixels with mixed membership. Full unmixing and the partial unmixing methods orthogonal subspace projection (OSP), constrained energy minimization (CEM) and an eigenvalue formulation alternative are dealt with. The solution to the eigenvalue formulation alternative proves to be identical to the CEM solution. Also, spectral angle mapping (SAM) is described. The matrix inversion involved in CEM can be avoided by working on (a subset of) orthogonally transformed data such as signal maximum autocorrelation factors, MAFs, or signal minimum noise fractions, MNFs. This will also cause the noise isolated in the MAF/MNFs not included in the analysis not to influence the partial unmixing result. CEM and the eigenvalue formulation alternative enable us to perform partial unmixing when we know the desired end-member spectra only and not the full set of endmember spectra. This is an advantage over full unmixing and OSP. An example with a simple generated 2-band image shows the ability of the CEM method to isolate the desired signal. A case study with a 30-band subset of AVIRIS data from the Mojave Desert, California, USA, shows the utility of the methods to more realistic data.